Single-mode optical fiber

ABSTRACT

A single-mode optical fiber has a prescribed mode field diameter (MFD 1  (μm)) at a first wavelength λ 1 , in which a bending loss when measured at a second wavelength λ 2  (μm) and wound with a bending radius r (mm) is L b  (dB) for one bending, a connector/splice loss with an optical fiber that has a prescribed mode field diameter MFD 2  (μm) at the first wavelength λ 1  is L s  (dB) for one connection/splice point at the second wavelength λ 2  (μm), and an mode field diameter dependence of a total loss coefficient calculated by a formula (1) has a local minimal value in a range of MFD 1 ±0.5 μm, with the formula (1) being as follows:
 
 L=w   s   ·L   s   +w   b   ·L   b ,  (1)
 
 w   s   +w   b =1,  (2)
 
w s &gt;0, w b &gt;0  (3)
 
where w s  and w b  in the formula (1) represent dimensionless weighting factors and are set within a range that satisfies the formulas (2) and (3).

This is a Continuation Application of International Application No.PCT/JP2005/014560, filed Aug. 9, 2005, which claims priority to JapanesePatent Application No. 2004-233111, filed on Aug. 10, 2004 and JapanesePatent Application No. 2005-120996 filed Apr. 19, 2005, the contents ofwhich are entirely incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a single-mode optical fiber(hereinafter, referred to as an SMF) that is excellent in bendingcharacteristics and connector/splice characteristics, and can bepreferably used as an optical fiber for which low bending loss isespecially required, such as in optical access or small component uses.

BACKGROUND ART

Conventionally, developments of a transmission system and an opticalfiber that use Wavelength Division Multiplexing (WDM) have been activelyadvanced with the objective of increasing the data transmission rate inbackbone and/or long-distance systems. The characteristics such assuppression of the nonlinear effect or chromatic dispersion control havebeen demanded for optical fibers for WDM transmission. In recent years,optical fibers in which the dispersion slope is decreased for a systemcalled metro (metropolitan area network) with a span of about severalkilometers or optical fibers that are subjected to virtually no lossincrease due to Hydroxyl Group (OH) have been proposed.

When introduction of optical fibers to offices and homes (Fiber To TheHome; FTTH) is taken into consideration, characteristics different fromthose for the above-described optical fibers for transmission arerequired. In the case of wiring the fibers in the building or the house,there is the possibility that a very small bending with a diameter suchas 30 mm or 20 mm occurs. Furthermore, when the extra length of thecable is stored, it is very important that a loss increase does notoccur even if the cable is wound around a small radius. That is, it is avery important characteristic for the optical cable for FTTH to resist asmall-radius bend. The connectivity with optical fibers (many of whichare SMFs with a normal bandwidth of 1.3 μm) used from the base stationto the building or to the house is also an important point.

Patent Document 1: U.S. Patent Application Publication No. 2004/0213531

Patent Document 2: PCT International Publication No. WO 01/27667pamphlet

Non-Patent Document 1: I. Sakabe, et al., “Enhanced Bending LossInsensitive Fiber and New Cables for CWDM Access Network,” Proceedingsof the 53rd IWCS, pp. 112-118 (2004)

Non-Patent Document 2: S. Matsuo et al., “Bend-insensitive andlow-splice-loss optical fiber for indoor wiring in FTTH,” OFC 2004, ThI3

Non-Patent Document 3: Sato et al., “Optical Fiber Conforming to Bendingaround Small Radius for Optical Access,” The Institute of Electronics,Information and Communication Engineers (IEICE) Society Conference 2003,B-10-30

Non-Patent Document 4: Ikeda et al., “Low Bending Loss Optical Fiberwith Reduced Splice Loss,” Technical Report of IEICE, OCS 2003-43

Non-Patent Document 5: Zhou et al., “A Study on Application of PhotonicCrystal Fiber to Wiring in Homes and Buildings,” Technical Report ofIEICE, OFT 2002-81

Non-Patent Document 6: Yao et al., “A Study on Commercialization ofHoley Fiber,” Technical Report of IEICE, OFT2002-82

DISCLOSURE OF INVENTION

Problem to be Solved by the Invention

Conventionally, in offices and homes, normal SMFs with a bandwidth of1.3 μm or multimode optical fibers are generally used. However, theseconventional optical fibers have generally allowed bending diametersdown to about 60 mm. In the wiring of the fibers, close attention hasbeen required to eliminate extra bending.

Furthermore, recently, SMFs have been commercialized that permitallowable bending diameters down to 30 mm by reducing the mode fielddiameter (hereafter, referred to as MFD) within a range complying withITU-T G.652, the international standard for the SMF for 1.3 μmbandwidth. However, SMFs that conform to bendings around a smallerradius are desirable for wiring in buildings and homes.

However, an SMF with enhanced bending characteristics generally has aproblem in that it has a small MFD, thus worsening the connector/splicecharacteristics.

That is, a parameter that works as an index to determine the optimaloptical fiber in an environment that assumes a small-radius bend has notbeen known.

The present invention has been achieved in view of such circumstances,and has an object to provide an SMF whose loss characteristics becomeoptimal in a line assumed to be bent in small radius.

Means for Solving the Problem

To achieve the above-mentioned object, the present invention provides anSMF, having a prescribed MFD (MFD₁ (μm)) at a first wavelength λ₁, inwhich a bending loss when measured at a second wavelength λ₂ (μm) andwound with a bending radius r (mm) is L_(b) (dB) for one bending (turn),a connector/splice loss with an optical fiber that has a prescribed MFD(MFD₂ (μm)) at the first wavelength λ₁ is L_(s) (dB) for oneconnection/splice point at the second wavelength λ₂ (μm), and an MFDdependence L of a total loss coefficient calculated by a formula (1) hasa local minimal value in a range of MFD₁±0.5 μm, with the formula (1)being as follows:L=w _(s) ·L _(s) +w _(b) ·L _(b),  (1)w _(s) +w _(b)=1,  (2)w_(s)>0, w_(b)>0,  (3)where w_(s) and w_(b) in the formula (1) represent dimensionlessweighting factors and are set within a range that satisfies the formulas(2) and (3).

Furthermore, the present invention provides an SMF, having a prescribedMFD (MFD₁ (μm)) at a first wavelength λ₁, in which a bending loss whenmeasured at a second wavelength λ₂ (μm) and wound with a bending radiusr (mm) is L_(b) (dB) for one bending, the number of bendings is t_(b), aconnector/splice loss with an optical fiber that has a prescribed MFD(MFD₂ (μm)) at the first wavelength λ₁ is L_(s) (dB) for oneconnection/splice point at the second wavelength λ₂ (μm), the number ofconnector/splice points is n_(s), and an MFD dependence of a total losscoefficient L calculated by a formula (4) has a local minimal value in arange of MFD₁±0.5 μm, with the formula (4) being as follows:L=n _(s) ·L _(s) +t _(b) ·L _(b)  (4)where n_(s)>0, t_(b)>0.

In the SMF of the present invention, it is preferable that theconnector/splice loss L_(s) be 0.5 dB or less.

In the SMF of the present invention, it is preferable that an amount ofvariation in total loss coefficient L when the MFD₁ is changed by ±0.3μm be 0.4 dB or less. It is further preferable that the amount ofvariation be 0.2 dB or less.

In the SMF of the present invention, it is preferable that the bendingradius r be less than 15 mm.

In the SMF of the present invention, it is preferable that the bendingloss L_(b) be 0.05 dB or less with the bending radius r=10 mm and thesecond wavelength λ₂=1550 nm.

In the SMF of the present invention, it is preferable that the bendingloss L_(b) be 0.05 dB or less with the bending radius r=7.5 mm and thesecond wavelength λ₂=1550 nm.

It is preferable that the SMF of the present invention include: acentral core that has a radius r₁ and a refractive index n₁; and acladding with a substantially constant refractive index n_(c) thatsurrounds the central core, where n₁>n_(c).

It is preferable that the SMF of the present invention include: acentral core that has a radius r₁ and a refractive index n₁; an innercladding that is provided around the outer circumference of the centralcore and has a radius r₂ and a refractive index n₂; a trench that isprovided around the outer circumference of the inner cladding and has aradius r₃ and a refractive index n₃; and an outer cladding that isprovided around the outer circumference of the trench and has a radiusr_(c) and a refractive index n_(c), where n₁>n_(c)>n₃, n₁>n₂>n₃.

In the SMF of the present invention, it is preferable that the firstwavelength λ₁=1310 nm and that the MFD₂ be in the range that satisfiesthe specifications under the international standard ITU-T G.652.

In the SMF of the present invention, it is preferable that theconnector/splice loss be a splice loss measured with each of the opticalfibers mechanically spliced.

In the SMF of the present invention, it is preferable that theconnector/splice loss be a splice loss measured with each of the opticalfibers fusion-spliced.

In the SMF of the present invention, it is preferable that theconnector/splice loss be a connection loss measured with each of theoptical fibers connected with a connector.

In the SMF of the present invention, it is preferable that the diameterof the cladding be within 125 μm±1 μm.

In the SMF of the present invention, it is preferable that the centervalue for the diameter of the cladding be in a range of 60 μm to 100 μm.

Furthermore, the present invention provides an SMF, having a prescribedMFD (MFD₁ (μm)) at a first wavelength λ₁, in which a bending loss whenmeasured at a second wavelength λ₂ (μm) and wound with a bending radiusr (mm) is L_(b) (dB) for one bending, a connector/splice loss with anoptical fiber that has a prescribed MFD (MFD_(2i) (μm)) at the firstwavelength λ₁, is L_(si) (dB) for one connection/splice point at thesecond wavelength λ₂ (μm), and an MFD dependence of a total losscoefficient L calculated by a formula (A) has a local minimal value in arange of MFD₁±0.5 μm, the formula (A) being as follows:

$\begin{matrix}{{L = {{\sum\limits_{i}^{n}{w_{si} \cdot L_{si}}} + {w_{b} \cdot L_{b}}}}{{{\sum\limits_{i = 1}^{n}w_{si}} + w_{b}} = 1}{{w_{si} > 0},{w_{b} > 0}}} & (A)\end{matrix}$where n represents the number of optical fibers that are connected withthe SMF of the present invention, w_(si) represents a dimensionlessweighting coefficient, and L_(si) represents a connector/splice loss(dB) between the SMF of the present invention and the i-th opticalfiber.

Furthermore, the present invention provides an SMF, having a prescribedMFD (MFD₁ (μm)) at a first wavelength λ₁, in which a bending loss whenmeasured at a second wavelength λ₂ (μm) and wound with a bending radiusr (mm) is L_(b) (dB) for one bending, the number of bendings is t_(b), aconnector/splice loss with an optical fiber that has a prescribed MFD(MFD_(2i) (μm)) at the first wavelength λ₁ is L_(si) (dB) for oneconnection/splice point at the second wavelength λ₂ (μm), the number ofconnection/splice points is n_(si), and an MFD dependence of a totalloss coefficient L calculated by a formula (B) has a local minimal valuein a range of MFD₁±0.5 μm, the formula (B) being as follows:

$\begin{matrix}{L = {{\sum\limits_{i = 1}^{n}{n_{si} \cdot L_{si}}} + {t_{b} \cdot L_{b}}}} & (B)\end{matrix}$where n represents the number of optical fibers that are connected withthe SMF of the present invention, n_(si) represents the connection timesbetween the SMF of the present invention and the i-th optical fiber, andL_(si) represents a connector/splice loss (dB) between the SMF of thepresent invention and the i-th optical fiber.

In the SMF of the present invention, it is preferable that theconnector/splice loss L_(si) be 0.1 dB or less.

In the SMF of the present invention, it is preferable that a variationin total loss coefficient L when the MFD₁ is changed by ±0.3 μm be 0.4dB or less.

In the SMF of the present invention, it is preferable that a variationin total loss coefficient L when the MFD₁ is changed by ±0.3 μm be 0.2dB or less.

Effects of the Invention

The SMF of the present invention can realize a stable opticaltransmission that has a small variation in loss with respect to a statechange under a condition of use that demands consideration of lossoccurrence resulting from a small-radius bend and a connection with anormal SMF.

The SMF of the present invention is configured such that losscharacteristics become optimal in a line assumed to be bent around asmall radius. Therefore, it can be preferably used as an SMF for whichlow loss in bending around a small radius is especially required, suchas in optical access or small component uses.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing a single-peak-type refractive index profile ofthe SMF of the present invention.

FIG. 2 is a graph of MFD dependence of bending loss (single-peak-type,r=10 mm), which shows a result of Example 1.

FIG. 3A is a schematic block diagram showing a connection configurationassumed for indoor wiring.

FIG. 3B is a schematic block diagram showing another connectionconfiguration assumed for indoor wiring.

FIG. 4 is a graph of MFD dependence of connector/splice loss, whichshows a result of Example 1.

FIG. 5 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 1.

FIG. 6 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 1.

FIG. 7 is a graph of MFD dependence of bending loss (single-peak-type,r=7.5 mm), which shows a result of Example 1.

FIG. 8 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 2.

FIG. 9 is another graph of MFD dependence of a total loss coefficient,which shows a result of Example 2.

FIG. 10 is a graph showing a trench-type refractive index profile of theSMF of the present invention.

FIG. 11 is a graph of MFD dependence of bending loss (r=10 mm), whichshows a result of Example 3.

FIG. 12 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 3.

FIG. 13 is another graph of MFD dependence of a total loss coefficient,which shows a result of Example 3.

FIG. 14 is a graph of MFD dependence of bending loss (r=7.5 mm), whichshows a result of Example 4.

FIG. 15 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 4.

FIG. 16 is a graph of MFD dependence of a total loss coefficient, whichshows a result of Example 4.

FIG. 17A is a graph exemplifying another refractive index profile of theSMF of the present invention.

FIG. 17B is a graph exemplifying another refractive index profile of theSMF of the present invention.

FIG. 17C is a graph exemplifying another refractive index profile of theSMF of the present invention.

FIG. 17D is a graph exemplifying another refractive index profile of theSMF of the present invention.

FIG. 17E is a graph exemplifying another refractive index profile of theSMF of the present invention.

FIG. 17F is a graph exemplifying another refractive index profile of theSMF of the present invention.

DESCRIPTION OF SYMBOLS

1: core; 2: cladding; 3: inner cladding; 4: trench; 5: outer cladding;6: inner cladding; 7, 8: outer core; 9: first trench; 10: low refractiveindex region; 11: electric pole; 12: closure; 13: branch cable; 14: dropcable; 15: ONU; 16: cabinet; 17: indoor cable; 18: wall; 19: cord withconnectors; 20: optical connector; 100, 200, 300A, 300B, 300C, 300D,300E, 300F: SMF

BEST MODE FOR CARRYING OUT THE INVENTION

Hereunder is a description of embodiments of the SMF of the presentinvention.

A first embodiment of the SMF of the present invention is characterizedby having a prescribed MFD (MFD₁ (μm)) at a first wavelength λ₁, inwhich a bending loss when measured at a second wavelength λ₂ (μm) andwound with a bending radius r (mm) is L_(b) (dB) for one bending, aconnector/splice loss with an optical fiber that has a prescribed MFD(MFD₂ (μm)) at the first wavelength λ₁ is L_(s) (dB) for oneconnection/splice point at the second wavelength λ₂ (μm), and an MFDdependence of a total loss coefficient L calculated by a formula (1) hasa local minimal value in a range of MFD₁±0.5 μm, with the formula (1)being as follows:L=w _(s) ·L _(s) +w _(b) ·L _(b),  (1)where w_(s) and w_(b) represent dimensionless weighting factors and areset within a range that satisfies the following formulas (2) and (3):w _(s) +w _(b)=1,  (2)w_(s)>0, w_(b)>0,  (3).

A second embodiment of the SMF of the present invention is characterizedby having a prescribed MFD (MFD₁ (μm)) at a first wavelength λ₁, inwhich a bending loss when measured at a second wavelength λ₂ (μm) andwound with a bending radius r (mm) is L_(b) (dB) for one bending, thenumber of bendings is t_(b), a connector/splice loss with an opticalfiber that has a prescribed MFD (MFD₂ (μm)) at the first wavelength λ₁is L_(s) (dB) for one connection/splice point at the second wavelengthλ₂ (μm), the number of connector/splice points is n_(s), and an MFDdependence of a total loss coefficient L calculated by a formula (4) hasa local minimal value in a range of MFD₁±0.5 μm, with the formula (4)being as follows:L=n _(s) ·L _(s) +t _(b) ·L _(b)  (4)where n_(s)>0, t_(b)>0.

The SMF of the present invention, which is designed by the use of atotal loss coefficient L calculated from the formula (1) or the formula(4), can realize a stable optical transmission that has a smallvariation in loss with respect to a state change under a condition ofuse that demands consideration of loss occurrence resulting from asmall-radius bending and a connection with a normal SMF.

In the first and second embodiments, there may be cases in which an MFD₂of an optical fiber that is connected with the SMF of the presentinvention may have a plurality of values. For example, in a normalprocess of an optical fiber manufacturing, an MFD can be evaluated in acondition that a median value in manufacture (an average value of MFDsof optical fibers manufactured) is regarded as an MFD₂ (μm).Furthermore, there may be cases in which the SMF of the presentinvention is connected with an optical fiber that has an MFD with adifferent median value in manufacture. For example, when the SMF of thepresent invention is applied to a drop cable 14 in FIG. 3A, thefollowing two cases can be conceived. One is a case in which an MFD withthe same MFD is used for both a branch cable 13 and an optical networkunit (ONU), which corresponds to the first and second embodiments. Theother is a case in which an SMF with enhanced bend-resistance having anMFD smaller than that for a normal SMF as described above is used in aconnection portion of the ONU. While the median value in manufacture ofthe MFD for a normal SMF is about 9.2 μm at 1310 nm, the median value inmanufacture of the MFD for an SMF with enhanced bend-resistance is about8.6 μm. In such a case, it is possible to handle the decrease in MFD bymodifying the formula (1) and the formula (4) as below.

The formula (1) can be modified as the following formula (A):

$\begin{matrix}{{L = {{\sum\limits_{i}^{n}{w_{si} \cdot L_{si}}} + {w_{b} \cdot L_{b}}}}{{{\sum\limits_{i = 1}^{n}w_{si}} + w_{b}} = 1}{{w_{si} > 0},{w_{b} > 0}}} & (A)\end{matrix}$where n represents the number of optical fibers that are connected withthe SMF of the present invention, w_(si) represents a dimensionlessweighting coefficient, and L_(si) represents a connector/splice loss(dB) between the SMF of the present invention and the i-th opticalfiber.

The formula (4) can be modified as the following formula (B):

$\begin{matrix}{L = {{\sum\limits_{i = 1}^{n}{n_{si} \cdot L_{si}}} + {t_{b} \cdot L_{b}}}} & (B)\end{matrix}$where n represents the number of optical fibers that are connected withthe SMF of the present invention, n_(si) represents the connection timesbetween the SMF of the present invention and the i-th optical fiber, andL_(si) represents a connector/splice loss (dB) between the SMF of thepresent invention and the i-th optical fiber.

The above-mentioned first wavelength λ₁ and second first wavelength λ₂can be selected from an optical transmission wavelength region using theSMF. For example, they can be selected from a range of 1260 nm to 1650nm. The wavelength range of 1260 nm to 1625 nm is used for an SMFtransmission. The wavelength range of 1625 nm to 1650 nm is used formonitoring the lines.

The above-mentioned bending radius r can be a radius bent around a smallradius assumed in real use of the SMF of the present invention. It ispreferable that the bending radius r be less than 15 mm.

In the SMF of the present invention, it is preferable that a bendingloss L_(b) for one bending measured with a bending radius r=7.5 mm or 10mm and a second wavelength λ₂=1550 nm, which is an estimation wavelengthfor a bending loss, be 0.05 dB or less. The bending loss L_(b) exceeding0.05 dB is not preferable because a loss increases due to a plurality ofsmall-radius bendings.

The above-mentioned connector/splice loss is measured in a conditionthat the SMF of the present invention is connected with an SMF used asan ordinary optical line (hereafter, referred to as a normal SMF) bymeans of a mechanical splice, a fusion splice, or a connector. In theSMF of the present invention, it is preferable that the connector/spliceloss L_(s) for one connection/splice point measured at the secondwavelength λ₂ (μm) be 0.5 dB or less. The connection/splice loss L,exceeding 0.5 dB is not preferable because a loss increases when thereare a plurality of connector/splice points. Note that a normal SMF to beconnected with the SMF of the present invention is often an SMF for a1.3 μm band under the international standard ITU-T G.652.

As for the SMF of the present invention, it is only required thatvarious parameters such as a core diameter, an MFD, a relative indexdifference between the core and the cladding, and a refractive indexprofile in the radial direction are set such that an MFD dependence of atotal loss coefficient L calculated by the formula (1) or (4) has alocal minimal value in a range of MFD₁±0.5 μm. The material, shape ofthe refractive index profile and the like can be set appropriately. Asfor the material for the SMF, silica glass or the like can be used, asis the case with the normal SMF. The SMF of the present invention can bemanufactured by various conventional, known methods, as is the case withthe manufacturing methods for the normal SMF.

FIG. 1 is, as an example of the SMF of the present invention, a graphshowing a single-peak-type (step-type) refractive index profile.

An SMF 100 of the present invention with this single-peak-typerefractive index profile includes: a central core 1 that has a radius r₁and a refractive index n₁; and a cladding 2 with a substantiallyconstant refractive index n_(c) that surrounds the central core 1, wheren₁>n_(c). It is preferable that the diameter of the cladding 2 be within125 μm±1 μm. Furthermore, the center value for the cladding diameter isnot limited to 125 μm. For example, in an optical fiber that requires avery small bending radius such as r=5 mm, it is effective to make thecladding diameter small for decreasing the probability of fatiguefailure. Therefore, the center value for the cladding diameter can beappropriately set in the range of 60 μm to 100 μm according to theconditions of use of the optical fiber.

FIG. 10 is, as another example of the SMF of the present invention, agraph showing a trench-type refractive index profile.

An SMF 200 of the present invention with this trench-type refractiveindex profile includes: a central core 1 that has a radius r₁ and arefractive index n₁; an inner cladding 3 that is provided around theouter circumference of the central core 1 and has a radius r₂ and arefractive index n₂; a trench 4 that is provided around the outercircumference of the inner cladding 3 and has a radius r₃ and arefractive index n₃; and an outer cladding 5 that is provided around theouter circumference of the trench 4 and has a radius r_(c) and arefractive index n_(c), where n₁>n_(c)>n₃, n₁>n₂>n₃. It is preferablethat the diameter of the outer cladding 5 be within 125 μm±1 μm. Thecenter value for the cladding diameter is not limited to 125 μm but canbe appropriately set in the range of 60 μm to 100 μm.

Furthermore, the present invention is applicable to SMFs with variousrefractive index profiles shown in FIGS. 17A to 17F.

An SMF 300A shown in FIG. 17A includes a single-peak-type central core 1and a two-layered cladding, in which an inner cladding 6 has a higherrefractive index than an outer cladding 5.

An SMF 300B with the refractive index profile shown in FIG. 17B isprovided with an outer cladding 5 outside a central core 1 with atrapezoidal refractive index profile, and includes an outer core 7 witha high refractive index spaced apart from the central core 1.

An SMF 300C with the refractive index profile shown in FIG. 17C isconfigured such that outside a center core 1 with a triangularrefractive index profile is provided with an inner cladding 6 with a lowrefractive index, an outer core 8 with a high refractive index, a trench4 with the lowest refractive index, and an outer cladding 5 with a lowrefractive index, in this order.

An SMF 300D with the refractive index profile shown in FIG. 17D isconfigured such that outside a central core 1 with an inverted U-shapedrefractive index profile is provided with a trench 4 with a lowrefractive index and an outer cladding 5 with a low refractive index, inthis order.

An SMF 300E with the refractive index profile shown in FIG. 17E isconfigured such that outside a central core 1 with a trapezoidal ortriangular refractive index profile is provided with a first trench 9with the lowest refractive index, an outer core 8 with a high refractiveindex, a second trench 4 with a low refractive index, and an outercladding 5 with a low refractive index, in this order.

An SMF 300F with the refractive index profile shown in FIG. 17F isconfigured in the same manner as in FIG. 17E, that is, it is configuredsuch that outside a central core 1 is provided with a first trench 9with the lowest refractive index, an outer core 8 with a high refractiveindex, a second trench 4 with a low refractive index, and an outercladding 5 with a low refractive index, in this order, the exceptionbeing that the central core 1 is constituted by a low refractive indexregion 10 at its central portion with a high refractive index regionthereoutside.

EXAMPLES Example 1

This example is designed for optimal characteristics with the assumptionthat the refractive index profile called a single-peak type as shown inFIG. 1 is used to apply bendings down to a 10-mm radius to the SMF 100.

The relationship, according to the single-peak-type refractive indexprofile, between an MFD at a wavelength of 1310 nm when a cable cut-offwavelength is set to 1260 nm and a bending loss when 10 bendings areapplied with a 10-mm radius at a wavelength of 1550 nm is shown in FIG.2.

As shown in FIG. 2, the larger the MFD is, the smaller the bending lossis. This FIG. 2 leaves an impression that a design for making the MFD assmall as possible is preferable for an SMF for use in a situation thatdemands resistance to bending.

In the real use environment, however, a connector/splice loss needs tobe taken into consideration in addition to a bending loss. FIGS. 3A and3B are figures exemplifying a configuration assumed for indoor wiring,in which reference numeral 11 denotes an electric pole, referencenumeral 12 a closure, reference numeral 13 a branch cable, referencenumeral 14 a drop cable, reference numeral 15 an ONU (Optical NetworkUnit), reference numeral 16 a cabinet, reference numeral 17 an indoorcable, reference numeral 18 a wall, reference numeral 19 a cord withconnectors, and reference numeral 20 an optical connector.

For example, in the form in which the drop cable 14 connected with thebranch cable in the closure 12 is directly connected with the ONU 15 asshown in FIG. 3A, there is the possibility that a connection withanother optical fiber is added in the closure 12. Furthermore, in theconnection with the ONU 15, there is the possibility that a connectionwith another optical fiber is added. When a wiring form as shown in FIG.3B is assumed, a use of a cord with connectors 19 that has a connectorat both of its ends can be conceived. In this case, there is thepossibility that a connection with another optical fiber is added at twopoints at worst.

A normal SMF defined under ITU-T G.652 is widely used for a branch cable13 and the like. Therefore, it is desirable that connection with thisnormal SMF be borne in mind for connection characteristics.

FIG. 4 shows a result of the evaluation of the connector/splice lossbetween the SMF 100 of the single-peak type (FIG. 1) and a normal SMF(MFD at a wavelength of 1310 nm is 9.2 μm). A connector/splice lossbetween optical fibers can be evaluated, as is shown in D. Marcuse,“Loss analysis of single-mode fiber splices”, Bell syst. Tech. J. vol.56, no. 5, p. 703, May, 1977, from the coupling efficiency calculatedfrom MFDs of two types of optical fibers by the use of the formula (5)as follows:T _(g)=(2·w ₁ ·w ₂/(w ₁ ² +w ₂ ²))²·exp(−2d ²/(w ₁ ² +w ₂ ²))  (5)where T_(g) represents a coupling efficiency, 2w₁ and 2w₂ each representan MFD of the respective optical fibers, and d represents an amount ofaxial displacement.

A connector/splice loss is caused by a difference in MFD, axialdisplacement of the field, or the like between two types of fibersconnected. Thus, as the difference in MFD is larger (in FIG. 4, as MFDdeviates further away from 9.2 μm), the connector/splice loss isgreater. Therefore, it is revealed that a design in which an MFD fallsbelow 6.5 μm is very stable in bending loss, but is very unstable inview of connection/splice.

FIG. 5 shows MFD dependence of a total loss coefficient evaluated by theformula (1), a technique of the present invention. Here, λ₁=1310 nm,λ₂=1550 nm, r=10 mm, MFD₂=9.2 μm, w_(s)=w_(b=0.5). FIG. 5 reveals thatthe total loss coefficient L is minimum with MFD₁=7.0 μm.

Accordingly, as for the SMF of MFD=6.5 μm (Sample 2) that is supposed tobe preferable in a design that takes a conventional bending loss as anindicator and the SMF of MFD=7.0 μm (Sample 1) that is evaluated aspreferable by the technique of the present invention, loss variations invarious circumstances were evaluated. The evaluation results are shownin Table 1. Note that in Tables 1 to 4, “evaluation condition” refers toa combination of connector/splice points and bendings.

TABLE 1 Evaluation Condition No. 1 2 3 4 5 6 7 8 Connector/Splice PointsMaximum Loss 1 1 1 1 2 2 2 2 Loss Variation Bendings Value Value 0 5 1020 0 5 10 20 [dB] [dB] Sample 1 0.33 0.36 0.39 0.45 0.66 0.69 0.72 0.780.78 0.45 Sample 2 0.53 0.53 0.53 0.54 1.06 1.06 1.06 1.07 1.07 0.54Sample 1 took Δ = 0.58%, r₁ = 3.26 μm, and Sample 2 took Δ = 0.65%, r₁ =3.07 μm, with Δ and r₁ as shown in FIG. 1. In both cases, the claddingdiameter was 125 μm, and the cable cut-off wavelength was 1260 nm.

The maximum value for the loss of Sample 1 produced by the technique ofthe present invention is suppressed to about 73% compared with that ofSample 2 by the conventional technique. Furthermore, it is revealed thatthe amount of variation in loss for Sample 1 is suppressed to about 83%in the assumed condition of use.

FIG. 6 shows MFD dependence of a total loss when two connector/splicepoints, r=10 mm, and 10 bendings are assumed. It is revealed that asubstantially minimum total loss is gained near the MFD of 7.0 μmdetermined by the technique of the present invention.

Furthermore, when the region determined by the technique of the presentinvention is used, the change in total loss due to the variation in MFDcan also be suppressed in a small range. For example, near MFD=7.0 μmdetermined by the technique of the present invention, the amount ofvariation in total loss is about 0.2 dB for an MFD change of about ±0.3μm. However, when the amount of variation in total loss is intended tobe suppressed to about the same degree in examples of the conventionaltechnique, virtually no variation in MFD will be recognized. On theother hand, when about the same degree of MFD variation is allowed, theamount of variation in total loss is about 0.8 dB, which is about 4times that of the case in which the technique of the present inventionis used.

The example above shows that in the SMF designed by the technique of thepresent invention, overall loss by bending and connection/splice issmall and that overall loss variation is very small even if variation inMFD of optical fibers, which is inevitable in manufacture, is assumed.This means that an application of the optical fiber of the presentinvention eliminates the need for an excessive margin in transmissionline design, thus enabling an efficient design.

Example 2

This example is designed for optimal characteristics with the assumptionthat the refractive index profile called a single-peak type as shown inFIG. 1 is used, as is the case with the above-mentioned Example 1, toapply bendings down to a 7.5-mm radius to the SMF 100.

The relation, according to the single-peak-type refractive indexprofile, between an MFD at a wavelength of 1310 nm when a cable cut-offwavelength is set to 1260 nm and a bending loss when 10 bendings areapplied with a 7.5-mm radius at a wavelength of 1550 nm (i.e., a bendingloss at a wavelength of 1550 nm with 10-turn bending of a 7.5-mm radius)is shown in FIG. 7. The larger the MFD is, the smaller the bending lossis. FIG. 7 leaves an impression, as is the case with r=10 mm, that adesign for making the MFD as small as possible is preferable for an SMFfor use in a situation that demands resistance to bending. As is alreadyshown in Example 1, however, there is a problem in such a region in thatthe connector/splice loss with a normal SMF is larger.

FIG. 8 shows MFD dependence of a total loss coefficient evaluated by theformula (1), a technique of the present invention. Here, λ₁=1310 nm,λ₂=1550 nm, bending radius r=7.5 mm, MFD₂=9.2 μm, w_(s)=w_(b)=0.5. FIG.8 reveals that the total loss coefficient L is minimum with MFD₁=6.8 μm.

Accordingly, as for the SMF of MFD=6.3 μm (Sample 4) that is supposed tobe preferable in a design that takes a conventional bending loss as anindicator and the SMF of MFD=6.8 μm (Sample 3) that is evaluated aspreferable by the technique of the present invention, loss variations invarious circumstances were evaluated. The evaluation results are shownin Table 2.

TABLE 2 Evaluation Condition No. 1 2 3 4 5 6 7 8 Connector/Splice PointsMaximum Loss 1 1 1 1 2 2 2 2 Loss Variation Bendings Value Value 0 5 1020 0 5 10 20 [dB] [dB] Sample 3 0.40 0.45 0.50 0.60 0.80 0.85 0.90 1.001.00 0.60 Sample 4 0.75 0.75 0.75 0.75 1.50 1.50 1.50 1.50 1.50 0.75Sample 3 took Δ = 0.61%, r₁ = 3.17 μm, and Sample 4 took Δ = 0.71%, r₁ =2.92 μm, with Δ and r₁ as shown in FIG. 1. In both cases, the claddingdiameter was 125 μm, and the cable cut-off wavelength was 1260 nm.

The maximum value for the loss of Sample 3 produced by the technique ofthe present invention is suppressed to about 66% compared with that ofSample 4 by the conventional technique. Furthermore, it is revealed thatthe amount of variation in loss for Sample 3 is suppressed to about 80%in the assumed condition of use.

FIG. 9 shows MFD dependence of a total loss when two connector/splicepoints, r=7.5 mm, and 10 bendings are assumed. It is revealed that asubstantially minimum total loss is gained near the MFD of 6.8 μmdetermined by the technique of the present invention.

Furthermore, when the region determined by the technique of the presentinvention is used, the change in total loss due to the variation in MFDcan also be suppressed in a small range. For example, near MFD=6.8 μmdetermined by the technique of the present invention, the amount ofvariation in total loss can be suppressed to about 0.2 dB if the MFD iscontrolled in the range of 6.60 to 6.95 μm. However, when the amount ofvariation in total loss is intended to be suppressed to about the samedegree in examples of the conventional technique, virtually no variationin MFD will be recognized. On the other hand, when about the same degreeof MFD variation is allowed, the amount of variation in total loss isabout 0.8 dB, which is about twice that of the case in which thetechnique of the present invention is used.

The example above shows that in the SMF designed by the technique of thepresent invention, overall loss by bending and connection/splice issmall and that overall loss variation is very small even if variation inMFD of optical fibers, which is inevitable in manufacture, is assumed.This means that an application of the optical fiber of the presentinvention eliminates the need for an excessive margin in transmissionline design, thus enabling an efficient design.

Example 3

This example is designed for optimal characteristics with the assumptionthat the refractive index profile as shown in FIG. 10 is used to applybendings down to a 10-mm radius to the SMF 200.

The relationship, according to the refractive index profiles shown inFIG. 1 and FIG. 10, between an MFD at a wavelength of 1310 nm when acable cut-off wavelength is set to 1260 nm and a bending loss when 10bendings are applied with a 10-mm radius at a wavelength of 1550 nm isshown in FIG. 11. It is revealed that the refractive index profile ofFIG. 10 can offer a smaller bending loss for the same MFD than therefractive index profile of FIG. 1. However, the tendency that thelarger the MFD is, the smaller the bending loss is, still persists.According to the conventional design technique that focuses attentiononly on the bending loss, 7.0 μm is preferable for the MFD.

FIG. 12 shows MFD dependence of a total loss coefficient evaluated bythe formula (1), a technique of the present invention. Here, λ₁=1310 nm,λ₂=1550 nm, bending radius r=10 mm, MFD₂=9.2 μm, w_(s)=w_(b)=0.5. FIG.12 reveals that the total loss coefficient L is minimum with MFD₁=8.2μm.

Accordingly, as for the SMF of MFD=7.0 μm (Sample 6) that is supposed tobe preferable in a design that takes a conventional bending loss as anindicator and the SMF of MFD=8.2 μm (Sample 5) that is evaluated aspreferable by the technique of this invention, loss variations invarious circumstances were evaluated. The evaluation results are shownin Table 3, together with the evaluation results of Samples 1 and 2 withthe refractive index profile of FIG. 1 shown in Example 1.

TABLE 3 Evaluation Condition No. 1 2 3 4 5 6 7 8 Connector/Splice PointsMaximum Loss 1 1 1 1 2 2 2 2 Loss Variation Bendings Value Value 0 5 1020 0 5 10 20 [dB] [dB] Sample 5 0.07 0.13 0.18 0.30 0.14 0.20 0.25 0.370.37 0.30 Sample 6 0.33 0.33 0.34 0.34 0.66 0.66 0.67 0.67 0.67 0.34Sample 1 0.33 0.36 0.39 0.45 0.66 0.69 0.72 0.78 0.78 0.45 Sample 2 0.530.53 0.53 0.54 1.06 1.06 1.06 1.07 1.07 0.54 Sample 5 took Δ₁ = 0.40%,Δ₂ = 0.0%, Δ₃ = −0.25%, r₁ = 3.56 μm, r₂ = 11.75 μm, r₃ = 17.80 μm, andSample 6 took Δ₁ = 0.54%, Δ₂ = 0.0%, Δ₃ = −0.25%, r₁ = 3.03 μm, r₂ =10.00 μm, r₃ = 15.15 μm, with Δ₁, Δ₂, Δ₃, r₁, r₂, and r₃ as shown inFIG. 10. In both cases, the cladding diameter was 125 μm, and the cablecut-off wavelength was 1260 nm.

The maximum loss value and amount of loss variation of Sample 5 areshown to be lower than those of Example 1 (Sample 1) in which thetechnique of the present invention is applied to the single-peak-typerefractive index profile. This result can be anticipated also from MFDdependence of a total loss in FIG. 12, and is an effect brought about byan improvement in refractive index profile. However, the maximum lossvalue of Sample 5 produced by applying the technique of the presentinvention to the trench-type refractive index profile is suppressed toabout 55% compared with that of Sample 6 by the conventional technique.Furthermore, the amount of loss variation of Sample 5 has improved by10% or more in the assumed condition of use. It is revealed that it hasimproved by about 33 to 65% compared with that by the conventionaldesign technique (Sample 2) for the single-peak-type profile.

FIG. 13 shows MFD dependence of a total loss when two connector/splicepoints and 10 bendings are assumed. It is revealed that a substantiallyminimum total loss is gained near the MFD of 8.2 μm determined by thetechnique of the present invention.

Also in this example, when the region determined by the technique of thepresent invention is used, the change in total loss due to the variationin MFD can also be suppressed in a small range. Even if an MFD variationof about ±0.3 μm is assumed, the change in total loss is very small,that is, 0.05 dB or less. When about the same degree of MFD variation isassumed in Sample 6 by the conventional design technique, a lossvariation of about 0.5 dB is anticipated.

The example above shows that in the SMF designed by the technique of thepresent invention, overall loss by bending and connection/splice issmall and that overall loss variation is very small even if variation inMFD of optical fibers, which is inevitable in manufacture, is assumed.This means that an application of the optical fiber of the presentinvention eliminates the need for an excessive margin in transmissionline design, thus enabling an efficient design.

Example 4

This example is designed for optimal characteristics with the assumptionthat the refractive index profile as shown in FIG. 10 is used to applybendings down to a 7.5-mm radius to the SMF 200.

The relationship, according to the refractive index profiles shown inFIG. 1 and FIG. 10, between an MFD at a wavelength of 1310 nm when acable cut-off wavelength is set to 1260 nm and a bending loss when 10bendings are applied with a 7.5-mm radius at a wavelength of 1550 nm isshown in FIG. 14. It is revealed that the refractive index profile ofFIG. 10 can offer a smaller bending loss for the same MFD than therefractive index profile of FIG. 1. However, the tendency that thelarger the MFD is, the smaller the bending loss is, still persists.According to the conventional design technique that focuses attentiononly on the bending loss, 6.8 μm is preferable for the MFD.

FIG. 15 shows MFD dependence of a total loss coefficient evaluated bythe formula (1), a technique of the present invention. Here, λ₁=1310 nm,λ₂=1550 nm, bending radius r=7.5 mm, MFD₂=9.2 μm, w_(s)=w_(b)=0.5. FIG.15 reveals that the total loss coefficient L is minimum with MFD₁=8.2μm.

Accordingly, as for the SMF of MFD=6.8 μm (Sample 8) that is supposed tobe preferable in a design that takes a conventional bending loss as anindicator and the SMF of MFD=7.2 μm (Sample 7) that is evaluated aspreferable by the technique of this invention, loss variations invarious circumstances were evaluated. The evaluation results are shownin Table 4, together with the evaluation results of Samples 3 and 4 forthe refractive index profile of FIG. 1 shown in Example 2.

TABLE 4 Evaluation Condition No. 1 2 3 4 5 6 7 8 Connector/Splice PointsMaximum Loss 1 1 1 1 2 2 2 2 Loss Variation Bendings Value Value 0 5 1020 0 5 10 20 [dB] [dB] Sample 7 0.26 0.31 0.36 0.46 0.52 0.57 0.62 0.720.72 0.46 Sample 8 0.42 0.43 0.44 0.45 0.84 0.85 0.86 0.88 0.88 0.46Sample 3 0.40 0.45 0.50 0.60 0.80 0.85 0.90 1.00 1.00 0.60 Sample 4 0.750.75 0.75 0.75 1.50 1.50 1.50 1.50 1.50 0.75 Sample 7 took Δ₁ = 0.52%,Δ₂ = 0.0%, Δ₃ = −0.25%, r₁ = 3.10 μm, r₂ = 10.23 μm, r₃ = 15.50 μm, andSample 8 took Δ₁ = 0.57%, Δ₂ = 0.0%, Δ₃ = −0.25%, r₁ = 2.94 μm, r₂ =9.70 μm, r₃ = 14.70 μm, with Δ₁, Δ₂, Δ₃, r₁, r₂, and r₃ as shown in FIG.10. In both cases, the claddin diameter was 125 μm, and the cablecut-off wavelength was 1260 nm.

The maximum loss value and the amount of the loss variation of Sample 7are shown to be lower than those of Example 2 (Sample 3) in which thetechnique of the present invention is applied to the single-peak-typerefractive index profile. This result is an effect brought about by animprovement in refractive index profile. As for Sample 7 produced byapplying the technique of the present invention to the trench-typerefractive index profile shown in FIG. 10, the amount of the lossvariation in the assumed condition of use is the same as that of Sample8 by the conventional technique, but the maximum loss value issuppressed to about 82% compared with that of Sample 8. It is revealedthat the maximum loss value and the amount of the loss variation aresuppressed to about half compared with those by the conventional designtechnique (Sample 4) for the single-peak-type profile of FIG. 1.

FIG. 16 shows MFD dependence of a total loss when two connector/splicepoints, r=7.5 mm, and 10 bendings are assumed. It is revealed that asubstantially minimum total loss is gained near the MFD of 7.2 μmdetermined by the technique of the present invention.

Also in this example, when the region determined by the technique of thepresent invention is used, the change in total loss due to the variationin MFD can also be suppressed in a small range. Even if an MFD variationof about ±0.2 μm is assumed, the change in the total loss is about 0.13dB. To suppress the loss variation within about the same degree in theconventional design region, only about ±0.05 μm is allowed for thechange in MFD. When an MFD variation of ±0.2 μm is assumed, a lossvariation of about 0.6 dB is anticipated.

The example above shows that in the SMF designed by the technique of thepresent invention, overall loss by bending and connection/splice issmall and that overall loss variation is very small even if variation inMFD of optical fibers, which is inevitable in manufacture, is assumed.This means that an application of the optical fiber of the presentinvention eliminates the need for an excessive margin in transmissionline design, thus enabling an efficient design.

In each of the above-described examples, 1310 nm was used as theevaluation wavelength for the MFD and 1550 nm was used as the evaluationwavelength for the bending loss. However, these wavelengths also are notparticularly limited by the examples. In each of the above-describedexamples, the MFD at a wavelength of 1310 nm was used for comparisonwith ITU-T G.652. On the other hand, the wavelength of 1550 nm belongsto the long wavelength side among the wavelengths now generally used foroptical communication. The bending loss of the optical fiber has atendency that the loss becomes worse as it goes further in the longwavelength side. Therefore, 1550 nm was used as the evaluationwavelength for the bending loss.

In each of the above-described examples, the calculated value from theformula (1) was used for the evaluation of the connector/splice loss.Using a measurement value of the connector/splice loss by a fusionsplice, a mechanical splice, a connector connection, or the like enablesthe optimization of the SMF with better precision.

Furthermore, in each of the above-described examples, cladding diameterwas 125 μm. However, the present invention is not limited to this. Forexample, to allow a bending with 5 mm or less, it is desirable that thecladding diameter be made smaller from the viewpoint of securingreliability. It is desirable that a cladding diameter of 60 to 100 μm beselected as required.

1. A single-mode optical fiber, having a prescribed mode field diameter(MFD₁ (μm)) at a first wavelength λ₁, wherein a bending loss whenmeasured at a second wavelength λ₂ (μm) and wound with a bending radiusr (mm) is L_(b) (dB) for one bending, a connector/splice loss with anoptical fiber that has a prescribed mode field diameter MFD₂ (μm) at thefirst wavelength λ₁ is L_(s) (dB) for one connection/splice point at thesecond wavelength λ₂ (μm), and an mode field diameter dependence of atotal loss coefficient L calculated by a formula (1) has a local minimalvalue in a range of MFD₁±0.5 μm, with the formula (1) being as follows:L=w _(s) ·L _(s) +w _(b) ·L _(b),  (1)w _(s) +w _(b)=1,  (2)w_(s)>0, w_(b)>0,  (3) where w_(s) and w_(b) in the formula (1)represent dimensionless weighting factors and are set within a rangethat satisfies the formulas (2) and (3).
 2. The single-mode opticalfiber according to claim 1, wherein the connector/splice loss L_(s) is0.5 dB or less.
 3. The single-mode optical fiber according to claim 1,wherein the bending radius r is less than 15 mm.
 4. The single-modeoptical fiber according to claim 3, wherein the bending loss L_(b) is0.05 dB or less with the bending radius r=10 mm and the secondwavelength λ₂=1550 nm.
 5. The single-mode optical fiber according toclaim 3, wherein the bending loss L_(b) is 0.05 dB or less with thebending radius r=7.5 mm and the second wavelength λ₂=1550 nm.
 6. Thesingle-mode optical fiber according to claim 1, comprising: a centralcore that has a radius r₁ and a refractive index n₁; and a cladding witha substantially constant refractive index n_(c) that surrounds thecentral core, where n₁>n_(c).
 7. The single-mode optical fiber accordingto claim 1, including: a central core that has a radius r₁ and arefractive index n₁; an inner cladding that is provided around the outercircumference of the central core and has a radius r₂ and a refractiveindex n₂; a trench that is provided around the outer circumference ofthe inner cladding and has a radius r₃ and a refractive index n₃; and anouter cladding that is provided around the outer circumference of thetrench and has a radius r_(c) and a refractive index n_(c), wheren₁>n_(c)>n₃, n₁>n₂>n₃.
 8. The single-mode optical fiber according toclaim 1, wherein the first wavelength λ₁=1310 nm and the mode fielddiameter MFD₂ is in a range that satisfies the specifications under theinternational standard ITU-T G.652.
 9. The single-mode optical fiberaccording to claim 1, wherein the connector/splice loss is a splice lossmeasured with each of the optical fibers mechanically spliced.
 10. Thesingle-mode optical fiber according to claim 1, wherein theconnector/splice loss is a splice loss measured with each of the opticalfibers fusion-spliced.
 11. The single-mode optical fiber according toclaim 1, wherein the connector/splice loss is a connection loss measuredwith each of the optical fibers connected with a connector.
 12. Thesingle-mode optical fiber according to claim 6, wherein the diameter ofthe cladding is within 125 μm±1 μm.
 13. The single-mode optical fiberaccording to claim 6, wherein the center value for the diameter of thecladding is in a range of 60 μm to 100 μm.
 14. The single-mode opticalfiber according to claim 7, wherein the diameter of the cladding iswithin 125 μm±1 μm.
 15. The single-mode optical fiber according to claim7, the center value for the diameter of the cladding is in a range of 60μm to 100 μm.
 16. A single-mode optical fiber, having a prescribed modefield diameter MFD₁ (μm) at a first wavelength λ₁, wherein a bendingloss when measured at a second wavelength λ₂ (μm) and wound with abending radius r (mm) is L_(b) (dB) for one bending, a connector/spliceloss with an optical fiber that has a prescribed mode field diameterMFD_(2i) (μm) at the first wavelength λ₁ is L_(si) (dB) for oneconnection/splice point at the second wavelength λ₂ (μm), and a modefield diameter dependence of a total loss coefficient L calculated by aformula (A) has a local minimal value in a range of MFD₁±0.5 μm, theformula (A) being as follows: $\begin{matrix}\begin{matrix}{L = {{\sum\limits_{i}^{n}\;{w_{si} \cdot L_{{si}\;}}} + {w_{b} \cdot L_{b}}}} \\{{{\sum\limits_{i = 1}^{n}\; w_{si}} + w_{b}} = 1} \\{{w_{si} > 0},{w_{b} > 0}}\end{matrix} & (A)\end{matrix}$ where n represents the number of optical fibers that areconnected with the single-mode optical fiber, w_(si) represents adimensionless weighting coefficient, and L_(si) represents aconnector/splice loss (dB) between the single-mode optical fiber and thei-th optical fiber.
 17. The single-mode optical fiber according to claim16, wherein the connector/splice loss L_(si) is 0.1 dB or less.
 18. Thesingle-mode optical fiber according to claim 16, wherein a variation intotal loss coefficient L when the MFD₁ is changed by ±0.3 μm is 0.4 dBor less.
 19. The single-mode optical fiber according to claim 18,wherein, a variation in total loss coefficient L when the MFD₁ ischanged by ±0.3 μm is 0.2 dB or less.